From the Editor: Coincidence, miracles and the Law of Truly Large Numbers

I recently purchased a low-price used book on Amazon.com and it arrived at the house by mail. The book cost a mere 50 cents, plus shipping, because it was a discarded, slightly soiled library book. I hadn't bothered to examine the tiny library name that was stamped on the inside cover. I just jumped right in and started reading the book.

Later, I grabbed a bookmark from a stack of bookmarks I have, a collection from various bookstores and libraries I have visited. The bookmark I had picked at random from the stack came from the Lee County Library in Cape Coral, Florida, which I had visited while on vacation there two years ago.

After I finished the first chapter, I stuck this randomly selected bookmark in place and then casually looked at where the used book originally came from. Well, much to my surprise, the inside book cover bore an official little stamp with a Magic Marker line of ink running across it: “Lee County Library, Cape Coral, Fla.” and the word “withdrawn”.

Was this a wild coincidence or something else?

Some call coincidences in life “little miracles”. It’s not much like walking on water, or healing the sick, but many people think there’s a divine hand behind such extraordinary occurrences in our lives which we are not meant to explain.

My recent bookmark incident made me recall one of the major, stand-out coincidences in my life.

When I was living in Tempe, Ariz., during the early 1980s, I was invited to attend a presentation at a Phoenix hotel about the personal use of biofeedback—that is, employing a small, electronic alpha-wave device to help a person relax or induce a positive state of mind.

Putting the validity of biofeedback aside, the speaker talked about how, by using his little $99 alpha box with headphones, it would help most everyone to get to sleep, even to support a meditation practice.

A short demonstration of the device followed, and although it was intriguing, I just couldn’t justify $99 for such a luxury item.

But the sales presentation called to mind Dave Worth, a college friend, who had used a similar alpha-wave box in our campus dormitory in 1972. He had used the device successfully to help relax before exams. I had lost touch with Dave when he moved to the West Coast to accept a job in the emerging home-computer industry.

I hadn’t thought of Dave, really, until the hotel sales pitch in Phoenix.

Flash forward just a few days to the annual downtown festival in Tempe.

Walking the sidewalk, I sampled Mexican and cowboy food, browsed various displays of pottery and colorful Southwestern art, and looked at Indian blankets and ponchos from Sonora. But then, I glimpsed a very familiar face in the sidewalk crowd—it was none other than Dave Worth.

We made eye contact, approached each other, and immediately reconnected by slapping each other on our backs.

Dave said he was visiting the Phoenix area on a business trip; he was working for a computer software company. We caught up on the years since our first- and second-year college days in Boston—we had both, later, transferred to different colleges to finish our undergraduate studies.

I told Dave about the biofeedback-box sales presentation I had witnessed and then talked a blue streak about the very mysterious coincidence of thinking of him and then having just run into him with no prior contact in eight years.

“It’s creepy,” I think I said. He laughed and agreed but said something about “the mystery of synchronicity.” I should mention that after that chance meeting in downtown Tempe, I never saw Dave Worth again.

Synchronicity, as it was defined by psychologist Carl Jung, is when two or more events are related in some deep, meaningful way. The idea of synchronicity is subjective, so there’s no real scientific test to either prove or disprove it. However, I have since learned that a few physicists have been looking into the idea as applied to the quantum foam, a transient, and root beer-like foamy construct which appears to make up the super small, sub-basement of our universe.

A quick look into the science of coincidence and miracles reveals that mathematics can explain these phenomena; so, if science is to be believed, there’s nothing spooky or supernatural involved.

“Correlation is not causation,” mathematicians studying chance are heard to say about all this. Thus, coincidence is simply the result of chance.

There’s also Littlewood's Law which focuses more on the science behind miracles in our lives. This law explains such occurrences with a complex mathematics of chance.

During the 1960s and ‘70s, British mathematician J. E. Littlewood (1885–1977) reported that “individuals should statistically expect one-in-a-million events (miracles) to happen to them at the rate of about one per month.”

So, I wonder, just how miraculous are miracles and amazing coincidences such as bumping into a long-lost friend you were just thinking about, or unknowingly sticking a two-year-old Cape Coral public library bookmark into a used book discarded from the same library?

I have always viewed such occurrences as evidence of something—maybe—bigger, deeper, and more mysterious than mere happenstance.

Littlewood reported that miracles are related to the Law of Truly Large Numbers. Hence. He wrote, “with a sample size large enough, any outrageous thing is likely to happen.” But what about that “defying the laws of nature” thing?

Even with science taking the wind out of super nature’s sails on a daily basis, it’s all still pretty amazing to me. If you understand numbers, maybe truly large numbers are an explanation you accept; but I still scratch my head and wonder.

So, now, what exactly are the odds?

Lou Varricchio/The Vermont Eagle

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